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Worksheet Grade 11 Science

Ilminster's Trihalomethanes: Water Age and Running Averages

A grade 11 worksheet on disinfection byproducts: students compute running annual averages at four sites, tie them to water age, and weigh a main-flushing program.

Objectives

  1. Students will calculate locational running annual averages and ranges from quarterly monitoring data.
  2. Students will relate disinfection byproduct concentrations to water age and water temperature.
  3. Students will evaluate three operating responses against pathogen safety and byproduct control.

Vocabulary

Disinfection byproduct (DBP)
A disinfection byproduct is a chemical that can form when disinfectants like chlorine react with natural organic matter in water. Treatment plants work to control disinfection byproducts because some of them can be harmful if people are exposed to too much over a long time.
Chlorine residual
Chlorine residual is the small amount of chlorine still left in the water after it leaves the treatment plant. It keeps protecting the water from germs all the way to your faucet.

Also: trihalomethane, water age, running annual average

Teacher overview

Chlorine reacts with natural organic matter in water to form trihalomethanes, and the reaction keeps going as the water sits in pipes and storage tanks. That makes disinfection byproducts a distribution problem rather than a plant problem: the same treated water carries different concentrations depending on how long it has been in the system. This worksheet gives students a year of quarterly results from four sampling sites in the fictional town of Ilminster, ordered by water age, and asks them to compute running annual averages, compare spread, and judge three possible responses. The misconception to address directly is the assumption that more chlorine is always safer. Utilities have to hold a residual through the whole system to control pathogens while keeping byproduct formation down, and those two goals pull the dose in opposite directions.

Ilminster's Trihalomethanes: Water Age and Running Averages — Grade 11 Science
Name: ____________________________ Date: ______________

Student Worksheet

Every item describes Ilminster, a fictional town. Ilminster's utility has set its own internal goal at 60 parts per billion for the annual average at any one site. Use this table throughout.

Site Average water age (days) Q1 Q2 Q3 Q4
A, near the plant 0.5 22 28 34 24
B, mid-system 1.2 34 42 51 37
C, system edge 3.4 48 58 74 52
D, dead-end main 6.1 62 79 96 67

All values are trihalomethanes in parts per billion.

  1. Site A recorded 22, 28, 34, and 24 parts per billion across the four quarters. Calculate its running annual average, which is the mean of the four quarterly results.
  2. Site D recorded 62, 79, 96, and 67 parts per billion. Calculate its running annual average.
  3. Ilminster's internal goal is 60 parts per billion for a site's annual average. Using your answers and the table, state which sites meet the goal and which do not.
  4. Calculate the range of Site A's four quarterly results.
  5. Calculate the range of Site D's four quarterly results.
  6. Compare your item 4 and item 5 answers together with the two annual averages. Describe what happens to both the center and the spread of the results as water age increases, and explain why the reaction between chlorine and organic matter produces that pattern.
  7. Site A's annual average is 27 parts per billion and Site D's is 76 parts per billion. Calculate the percent increase from Site A to Site D, rounded to the nearest tenth of a percent.
  8. Site A sits at 0.5 days of water age with an annual average of 27 parts per billion, and Site D sits at 6.1 days with 76 parts per billion. Calculate the average rate of increase in parts per billion per day of water age, rounded to the nearest hundredth.
  9. A flushing program would cut Site D's water age from 6.1 days to 2.8 days. Starting from Site A's 27 parts per billion at 0.5 days and using your item 8 rate, predict Site D's new annual average, rounded to the nearest tenth.
  10. Calculate the mean of the four sites' third-quarter results.
  11. Calculate the mean of the four sites' first-quarter results.
  12. Third-quarter samples are collected in August and first-quarter samples in February. Using your item 10 and item 11 answers, explain what water temperature has to do with the difference.
  13. One proposal is to lower the chlorine dose at the plant. Systems typically maintain a residual of 0.2 to 2.0 mg/L through the distribution system, and the maximum residual disinfectant level is 4.0 mg/L. Explain why cutting the dose is not a simple fix for Ilminster's Site D result.
  14. Ilminster can flush the dead-end main, increase turnover in its storage tank, or lower the plant dose. Recommend one action, name the criterion that decides it for you, and state one cost or drawback the town would accept by choosing it.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 27.0 parts per billion.
    (22 + 28 + 34 + 24) / 4 = 108 / 4 = 27.0 parts per billion.
  2. Answer: 76.0 parts per billion.
    (62 + 79 + 96 + 67) / 4 = 304 / 4 = 76.0 parts per billion.
  3. Answer: Sites A, B, and C meet the goal; Site D does not.
    Site A averages 27.0, Site B averages (34 + 42 + 51 + 37) / 4 = 41.0, and Site C averages (48 + 58 + 74 + 52) / 4 = 58.0, all at or below 60. Site D averages 76.0, which is above the goal.
  4. Answer: 12 parts per billion.
    34 - 22 = 12 parts per billion between Site A's highest and lowest quarters.
  5. Answer: 34 parts per billion.
    96 - 62 = 34 parts per billion between Site D's highest and lowest quarters.
  6. Answer: Both the center and the spread increase with water age.
    The annual average climbs from 27.0 at Site A to 76.0 at Site D, and the range widens from 12 to 34. Trihalomethanes form over time as chlorine keeps reacting with organic matter, so older water carries more of them, and the longer reaction time also lets seasonal differences in temperature and organic matter accumulate, which widens the quarter-to-quarter spread.
  7. Answer: 181.5 percent.
    (76 - 27) / 27 = 49 / 27 = 1.8148, or a 181.5 percent increase.
  8. Answer: 8.75 parts per billion per day.
    (76 - 27) / (6.1 - 0.5) = 49 / 5.6 = 8.75 parts per billion per day of water age.
  9. Answer: 47.1 parts per billion.
    Water age falls to 2.8 days, which is 2.8 - 0.5 = 2.3 days beyond Site A. 27 + (8.75 x 2.3) = 27 + 20.125 = 47.1 parts per billion, below the town's goal of 60.
  10. Answer: 63.75 parts per billion.
    (34 + 51 + 74 + 96) / 4 = 255 / 4 = 63.75 parts per billion.
  11. Answer: 41.5 parts per billion.
    (22 + 34 + 48 + 62) / 4 = 166 / 4 = 41.5 parts per billion.
  12. Answer: Warmer water speeds the reaction, so summer results run higher.
    The August mean of 63.75 is well above the February mean of 41.5. Reaction rates rise with temperature, and utilities also tend to carry a higher chlorine dose in warm weather, so both effects push summer trihalomethanes up.
  13. Answer: A lower dose risks losing the residual that controls pathogens.
    The plant has to deliver enough chlorine that a residual of roughly 0.2 to 2.0 mg/L still remains at the far end of the system, and Site D is the farthest point. Cutting the dose to reduce byproducts at Site D could leave that main with too little residual to suppress bacterial regrowth, which trades a long-term chemical risk for an immediate microbial one.
  14. Answer: Flushing the dead-end main, with a stated criterion and drawback.
    Accept any of the three actions when the reasoning is consistent. A strong answer names flushing, uses the item 9 prediction of 47.1 parts per billion as evidence that it brings Site D under the goal, cites pathogen safety as the criterion that rules out cutting the dose, and accepts the drawback that flushing discharges treated water that the town has already paid to produce. Answers choosing storage turnover should note that it lowers water age system-wide but requires operating changes at the tank, and answers choosing a dose reduction must address the residual requirement in item 13.

Differentiation

Support

Provide the annual averages already computed for Sites B and C so students can focus on Sites A and D, and give a number line marking the town's goal of 60 parts per billion with each site's average plotted on it. Supply the percent-increase formula with labeled blanks for the original and new values before item 7.

Extension

Have students plot annual average against water age for all four sites, fit a line, and compare its slope with the two-point rate from item 8. Ask them to explain which estimate they would give the utility and why using four points changes their confidence.

ELL supports

Pre-teach water age, residual, byproduct, and running annual average with a diagram tracing one gallon from the plant to a dead-end main, labeling how long it sits at each stage. Offer sentence frames for items 6, 12, and 13, such as "As water age increases, the average ___ because ___."